xenharmonic (microtonal wiki)

Omnitetrachordal MOS and MODMOS scale
12L+12s
24 tones (10+4+10)

catler, compton; 3 forms

Form 1 (MOS) has some unusual properties:

it has only two modes
either mode may be split in any of the three possible omnitetrachordal ways (9/8-4/3-4/3, 4/3-9/8-4/3, 4/3-4/3-9/8)
it is its own dual (changing all L to s, and vice versa, gives the same scale)

See also OTC 5L+5s (blackwood) and OTC 7L+7s (whitewood), which have similar properties.

For all 3 forms:

the (imperfect) tunings of 9/8 and 4/3 are independent of L/s ratio

Forms 2 and 3 are duals.

P = undefined (-1?)
Q = 24.5754362493 (4/3 = 5L+4.5s)

L = 50.00 to 100.00 cents (96.09 cents @ Q)
s = 0.00 to 50.00 cents (3.91 cents @ Q)

9/8 = 2L+2s (200.00 cents, for any L/s)
4/3 = 5L+5s (500.00 cents, for any L/s)
MOS generator = s (0.00 to 50.00 cents)
MOS period = 1/12 octave (100.00 cents)

notable EDOs: 36, 48, 60, 72, 84

LsLsLsLsLsLsLsLsLsLsLsLs (OTC form 1, MOS)
|    ||  ||    ||  ||  |
ssLsLLssLLssLsLLssLLssLL (form 2, MODMOS) - gc 3,3,3,2,3,3,2; 5o ;; pc 12,2,2; 8o
   ||        ||
ssLLsLssLLssLLsLssLLssLL (form 3, MODMOS) - gc 3,3,3,2,3,3,2; 5o ;; pc 12,2,2; 8o
|  ||||  ||  ||||  ||  |
LsLsLsLsLsLsLsLsLsLsLsLs (form 1)

all modes, form 1:

`LsLs LsLsLsLsLs LsLsLsLsLs`	`LsLsLsLsLs LsLs LsLsLsLsLs`	`LsLsLsLsLs LsLsLsLsLs LsLs`
`sLsL sLsLsLsLsL sLsLsLsLsL`	`sLsLsLsLsL sLsL sLsLsLsLsL`	`sLsLsLsLsL sLsLsLsLsL sLsL`

all modes, form 2:

		`ssLsLLssLL ssLsLLssLL ssLL`
		`sLsLLssLLs sLsLLssLLs sLLs`
		`LsLLssLLss LsLLssLLss LLss`
	`sLLssLLssL sLLs sLLssLLssL`	`sLLssLLssL sLLssLLssL LssL`
	`LLssLLssLs LLss LLssLLssLs`
	`LssLLssLsL LssL LssLLssLsL`
	`ssLLssLsLL ssLL ssLLssLsLL`
	`sLLssLsLLs sLLs sLLssLsLLs`
	`LLssLsLLss LLss LLssLsLLss`
	`LssLsLLssL LssL LssLsLLssL`
	`ssLsLLssLL ssLL ssLsLLssLL`
	`sLsLLssLLs sLLs sLsLLssLLs`
	`LsLLssLLss LLss LsLLssLLss`
`sLLs sLLssLLssL sLLssLLssL`	`sLLssLLssL LssL sLLssLLssL`
`LLss LLssLLssLs LLssLLssLs`
`LssL LssLLssLsL LssLLssLsL`
`ssLL ssLLssLsLL ssLLssLsLL`
`sLLs sLLssLsLLs sLLssLsLLs`		`sLLssLLssL sLLssLLssL sLLs`
`LLss LLssLsLLss LLssLsLLss`		`LLssLLssLs LLssLLssLs LLss`
`LssL LssLsLLssL LssLsLLssL`		`LssLLssLsL LssLLssLsL LssL`
`ssLL ssLsLLssLL ssLsLLssLL`		`ssLLssLsLL ssLLssLsLL ssLL`
`sLLs sLsLLssLLs sLsLLssLLs`		`sLLssLsLLs sLLssLsLLs sLLs`
`LLss LsLLssLLss LsLLssLLss`		`LLssLsLLss LLssLsLLss LLss`
`LssL sLLssLLssL sLLssLLssL`		`LssLsLLssL LssLsLLssL LssL`

all modes, form 3:

`ssLL sLssLLssLL sLssLLssLL`		`ssLLsLssLL ssLLsLssLL ssLL`
`sLLs LssLLssLLs LssLLssLLs`		`sLLsLssLLs sLLsLssLLs sLLs`
		`LLsLssLLss LLsLssLLss LLss`
		`LsLssLLssL LsLssLLssL LssL`
		`sLssLLssLL sLssLLssLL ssLL`
	`LssLLssLLs LssL LssLLssLLs`	`LssLLssLLs LssLLssLLs sLLs`
	`ssLLssLLsL ssLL ssLLssLLsL`
	`sLLssLLsLs sLLs sLLssLLsLs`
	`LLssLLsLss LLss LLssLLsLss`
	`LssLLsLssL LssL LssLLsLssL`
	`ssLLsLssLL ssLL ssLLsLssLL`
	`sLLsLssLLs sLLs sLLsLssLLs`
	`LLsLssLLss LLss LLsLssLLss`
	`LsLssLLssL LssL LsLssLLssL`
	`sLssLLssLL ssLL sLssLLssLL`
`LssL LssLLssLLs LssLLssLLs`	`LssLLssLLs sLLs LssLLssLLs`
`ssLL ssLLssLLsL ssLLssLLsL`
`sLLs sLLssLLsLs sLLssLLsLs`
`LLss LLssLLsLss LLssLLsLss`
`LssL LssLLsLssL LssLLsLssL`		`LssLLssLLs LssLLssLLs LssL`
`ssLL ssLLsLssLL ssLLsLssLL`		`ssLLssLLsL ssLLssLLsL ssLL`
`sLLs sLLsLssLLs sLLsLssLLs`		`sLLssLLsLs sLLssLLsLs sLLs`
`LLss LLsLssLLss LLsLssLLss`		`LLssLLsLss LLssLLsLss LLss`
`LssL LsLssLLssL LsLssLLssL`		`LssLLsLssL LssLLsLssL LssL`

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